The question of the closedness of the convex hull of the union of a closed convex set and a compact convex set in a locally convex space does not appear to be widely known. We show here that the answer is affirmative if and only if the closed convex set is bounded. The result is first proven for convex compact sets ”of finite type” (polytopes) using an induction argument. It is then extended to arbitrary convex compact sets using the fact that such subsets in locally convex spaces admit arbitrarily small continuous displacements into polytopes.
In the last decades cloud computing has been the focus of a lot of research in both academic and industrial fields, however, implementation-related issues have been developed and have received more attention than performance analysis which is an important aspect of cloud computing and it is of crucial interest for both cloud providers and cloud users. Successful development of cloud computing paradigm necessitates accurate performance evaluation of cloud data centers. Because of the nature of cloud centers and the diversity of user requests, an exact modeling of cloud centers is not practicable; in this work we report an approximate analytical model based on an approximate Markov chain model for performance evaluation of a cloud computing center. Due to the nature of the cloud environment, we considered, based on queuing theory, a MMPP task arrivals, a general service time for requests as well as large number of physical servers and a finite capacity. This makes our model more flexible in terms of scalability and diversity of service time. We used this model in order to evaluate the performance analysis of cloud server farms and we solved it to obtain accurate estimation of the complete probability distribution of the request response time and other important performance indicators such as: the Mean number of Tasks in the System, the distribution of Waiting Time, the Probability of Immediate Service, the Blocking Probability and Buffer Size…
In this work, we employ an enhanced (G' / G) -expansion method to study the nonlinear evolution equations (NLEEs). Here we derive exact traveling wave solutions for the modified Burgers-KDV equation. The obtained results show that the applied equation reveals richness of explicit soliton and periodic solutions. It has been shown that the enhanced (G' / G) -expansion method is effective and can be used for many other NLEEs in mathematical physics.
In this paper, we construct codes over rings which have a Euclidean division, in the commutative and non commutative cases. Such construction generalizes Reed-Solomon codes. We exemplify the construction for Gaussian integers and Lipschitz quaternions.
In this paper we take advantage of the known interpolation Least Square Method (LSM) to construct audio coding/decoding (CODEC) algorithms. The purpose of this algorithm is to compress audio data, maintain high quality audio, and enable sending/storing audio as serial data through digital transmission systems. Our proposed algorithms can be an efficient replacement for the quantization process used in many CODECs and modulations like PCM. We clarify our research by explaining the reasons, the assumptions, and the experiments' results for each step individually. We applied the algorithms to 20 audio files and introduced three algorithms that approach the most efficient compression ratio in addition to best signal to noise ratio. We showed Pseudo Codes, Flowcharts, and complete results of some experiments, and also a comparison with PCM used in telephony system.
All processes take time to complete. While physical processes such as acceleration and deceleration take little time compared to the times need to travel most distances, the times involved in biological processes such as gestation and maturation can be substantial when compared to the data-collection times in most population studies. Therefore, it is often imperative to explicitly incorporate these process times in mathematical models of population dynamics. These process times are often called delay times, and the model that incorporate such delay times are referred as delay differential equation (DDE) models. The models will examine some theoretical concepts and their applications to real life situation. The application examines measles and the time it takes to manifest or to its removal or treatment from the system. The solutions of the models will be displayed in graphical forms using MATLAB method. The analysis of the models indicate the times delay and its characteristics.
Aims: The aim of this paper is to investigate interval-valued hesitant multiplicative preference relations and their application to multi-criteria decision making. Study Design: Based on pseudo-multiplication, we define some basic operations for the interval-valued hesitant multiplicative sets (IVHMSs) and develop several aggregation operators for aggregating the interval-valued hesitant multiplicative information. Some desired properties and special cases of the developed operators are also investigated. Furthermore, we present a new preference structure named as the interval-valued hesitant multiplicative preference relation (IVHMPR), each element of which is an IVHMS, denoting all the possible interval multiplicative preference values offered by the decision makers for a paired comparison of alternatives. Place and Duration of Study: Interval-valued hesitant fuzzy set (IVHFS), recently introduced by Chen et al., permits the membership degree of an element to a set to be represented as several possible interval values. However, it is noted that IVHFS uses 0.1–0.9 scale, which is inconsistent with some practical problems (e.g. the law of diminishing marginal utility in economics). Methodology: We use the unsymmetrical 1–9 scale instead of the symmetrical 0.1–0.9 scale to express the membership degree information in the IVHFS and introduce the concept of interval-valued hesitant multiplicative set (IVHMS). Results: An approach for multi-criteria decision making based on the interval-valued hesitant multiplicative preference relations (IVHMPRs) is developed and some numerical examples are provided to illustrate the developed approach. Conclusion: We compare the IVHMPR with the interval-valued hesitant preference relation (IVHPR) and the interval multiplicative preference relation (IMPR), and show the effectiveness and practicality of the IVHMPR.
In this paper, we introduce k-fractional Hilfer derivative given in . A combination of fractional Fourier transform method and Laplace transform method is adopted to solve Cauchy-type problems involving k-fractional Hilfer derivatives and an integral operator whose kernel contains k-Mittag-Leffler function similar to the one given in . The solutions to these problems are obtained in terms of Mittag-Leffler function.
Survey research has been widely used in public opinion research in Ghana. Ghanaian researchers are happy about data richness and they are also concerned about data quality. In this paper Item Response Theory (IRT) has been used to identify the most appropriate IRT model for understanding item. The techniques are appropriate and practical. A questionnaire data on Ghana collected in the 5th wave of the World Values Survey was used for the analysis. The five categories of survey questions that are most difficult to answer by respondents were Life Related Questions, Value Related Questions, Political Related Questions, Income Related Questions and Democracy Related Questions. Missing or ‘don’t know’ responses were assigned a 0 score, and 1 was assigned to answered items. The data was analysed based on four IRT models namely, the constrained Rasch model, the unconstrained Rasch model, the two parameter logistic model, and the three parameter logistic model. These models were explored to determine the most appropriate model for the data. In this paper, the unconstrained Rasch model emerged as the best model for understanding item non-response. We found that, income related questions had the highest difficulty parameter, hence the most difficult category of survey questions to answer. It was also found that, if an individual does not answer a survey question or give a ‘don’t know’ answer, it is not only because of the question’s difficulty but also because the respondent doesn’t want to answer.